Scrappy how exactly? Apart from the lack of colour depth, GIFs can be as sharp as any format. It's all down to the save settings in your image editor.
I often use PNGs, which support transparency but have colour depth and resolution that are comparable with other formats.
Failing that; if you intend to place the GIF in fixed location relative to the background, you can copy the exact part of the background and use it as part of the image.